Evaluation of LS-DYNA Concrete Material Model 159

Appendix A. User Code Verification

Introduction

This task involved repeating the finite element calculations previously performed by the developer using input files supplied by the developer, and comparing the results of these calculations. Five models were supplied to the user by the developer. The models included a single element model (three load cases), concrete cylinder under tension, plain (unreinforced) concrete beam under impact loading, over-reinforced concrete beam under impact loading, and reinforced concrete beam under impact loading by surrogate vehicle.

All the input files incorporate the new material (MAT type 159 or MAT_CSCM) to be released in LS-DYNA version 971. The user obtained a beta binaries release of LS-DYNA version 971 for the following platforms/operating systems: SGI IRIX (version 971 release 1490 double precision ), MS-Windows (version 971 release 1612 single precision), and Linux Intel 32 bit architecture (version 971 release 1708 single precision). The SGI IRIX binary crashed with a floating point exception error during the initialization phase of reading an input file. The researchers believe the crash occurred because the SGI binary beta release (1490) might not be as "bug free" as the other binaries.

Case 1. Single Element Simulations

In this case, a single solid element was used to verify the basic behavior of the material model. There are three loading conditions for this case. The first load case was compression of the element as shown in Figures 148 and 149. The second load case was application of a tensile load to the element as shown in Figures 150 and 151. The last load case was a shear load applied on the element as shown in Figures 152 and 153. For each of these load conditions, the user calculations precisely matched the developer's calculations as Figures 148-153 indicate.

psi = 145.05 MPa

Figure 148. Single element under compressive loading, developer.

psi = 145.05 MPa

Figure 149. Single element under compressive loading, user.

psi = 145.05 MPa

Figure 150. Single element under tensile loading, developer.

psi = 145.05 MPa

Figure 151. Single element under tensile loading, user.

psi = 145.05 MPa

Figure 152. Single element under pure shear loading, developer.

psi = 145.05 MPa

Figure 153. Single element under pure shear loading, user.

Case 2. Cylinder Runs

This case consists of a plain unreinforced concrete cylinder subject to tensile loading. The tension loading was simulated by pulling both ends of the cylinder at a constant velocity. An inclined cross section was defined in the model to track force versus time, as shown in Figure 154 below.

Figure 154. Concrete cylinder model with inclined cross section.

Fringes of the damage to the materials were plotted at various times during the analysis. The damage parameter plotted is the maximum of brittle and ductile damage calculated by the material model. It is noteworthy that damage is a normalized entity from 0 (no damage) to 1.0 (complete damage).

Figures 155-157 show these damage fringe plots at key times. Figures 158 and 159 show the cross-sectional force versus time measured on the inclined plane from the developer calculation and the user calculation, respectively. The user calculations matched the developer's calculations in terms of both damage fringes and cross-sectional force for this model. Two binaries were used for this calculation; however, only the Windows results are presented because there was no significant difference between the computed results.

Figure 155. Damage fringe t = 13.498 msec.

Figure 156. Damage fringe t = 13.598 msec.

Figure 157. Damage fringe at t = 40 msec.

psi = 145.05 MPa

Figure 158. Cross-sectional force (developer).

psi = 145.05 MPa

Figure 159. Cross-sectional force (user).

Case 3. Plain Concrete Beam

In this case, an unreinforced concrete beam was modeled using the CSCM concrete model. Unlike previous cases, this model incorporates element erosion and contact definitions. The element erodes based on a set damage threshold above 0.99. Contacts were defined to represent surface interaction between parts (beam, impact parts, support parts, etc.).

Damage fringes were plotted at simulation times (t) of 1, 4, 20, and 30 msec. Figures 160-163 show the respective damage fringe plots obtained from the developer calculations for these simulation times. Figures 164-167 show the corresponding damage fringes plots from the user's calculations using the Linux binary. Similarly, Figures 168-171 show the respective damage fringe plots from the user's calculations using the Windows binary for the aforementioned simulation times.

At 1 msec of simulation time, the beam was already experiencing damage as shown in Figure 160 (developer), Figure 164 (user Linux), and Figure 168 (user Windows). The damage fringe from all three calculations looks very similar. Some elements were already eroded at t = 4 msec as shown in Figure 161 (developer), Figure 165 (user Linux), and Figure 169 (user Windows). Although the number of eroded elements is different among the three calculations, the fracture pattern is considered to be bounded within expected behavior of concrete. This same degree of variation in cracking patterns is observed among identical laboratory tests.

Figure 160. Plain concrete damage fringe at 1 msec (developer).

Figure 161. Plain concrete damage fringe at 4 msec (developer).

Figure 162. Plain concrete damage fringe at 20 msec (developer).

Figure 163. Plain concrete damage fringe at 30 msec (developer).

Figure 164. Plain concrete damage fringe t =1 msec (user Linux).

Figure 165. Plain concrete damage fringe t = 4 msec (user Linux).

Figure 166. Plain concrete damage fringe t = 20 msec (user Linux).

Figure 167. Plain concrete damage fringe t = 30 msec (user Linux).

Figure 168. Plain concrete damage fringe t = 1 msec (user Windows).

Figure 169. Plain concrete damage fringe t = 4 msec (user Windows).

Figure 170. Plain concrete damage fringe t = 20 msec (user Windows).

Figure 171. Plain concrete damage fringe t = 30 msec (user Windows).

Case 4. Reinforced Concrete Beam

In this case, an over-reinforced concrete beam was modeled using the CSCM concrete model. The setup is similar to the model used in case 3 with the exception that beam elements are added to model the steel reinforcement inside the concrete beam. Both Windows and Linux binaries were used for conducting calculations with this model. Due to their similarity to one another, only one set of results (from the Linux binary) is presented in this report. Figures 172-175 show the damage fringes plots obtained from the developer calculations at simulation times corresponding to 1, 4, 16, and 20 msec, respectively. Figures 176-179 show damage fringe plots from the user Linux's calculations using the same simulation times. Figures 180 and 181 show the displacement history plot of a node on the impacting heads using the developer and user calculations, respectively.

Due to the over-reinforced nature of the beam, element erosion did not initiate in this analysis case. Close correlation was obtained between the user and the developer calculations for both the damage fringes and the displacement history of the impactor node. The minor variations that exist are well within the anticipated range of behavior.

Case 5. Bogie Impact Tests

In the final case, another steel-reinforced concrete beam was modeled using the CSCM concrete model. The loading condition represents a bogie vehicle impacting the reinforced beam at a speed of 33 km/h (20.5 mi/h). Figures 182-185 show the damage fringes plots from developer calculations at simulation times of 4, 8, 48, and 80 msec, respectively. Figures 186-189 show damage fringes plots from user Windows binary calculations at these same simulation times. Figures 190-193 show the corresponding damage fringes plots from user Linux binary calculations.

As for the beam analyzed in case 3, the damage fringes for the impacted beam in the user calculations developed similarly to those obtained from the developer calculations, and the subsequent element erosion pattern representing the cracking and failure of the beam shows differences for each calculation. However, the element erosion/fracture patterns are bounded within the same physical regions of the beam and the differences are considered to be within normal variability and range of behavior expected of a concrete member of this type.